Conventionally, as shown in, e.g., Patent Document 1, an engine has been known in which, for the purpose of improving combustion or the like, an exhaust valve is opened (re-opened) during an intake stroke subsequently to the opening/closing thereof during an exhaust stroke to thereby introduce burnt gas (exhaust gas) in an exhaust passage as internal EGR gas into a cylinder. Also, in Patent Document 1, it is disclosed to open (pre-open) an intake valve during the exhaust stroke to introduce the burnt gas into an intake passage and to introduce the burnt gas, together with fresh air, as the internal EGR gas into the cylinder in the next intake stroke. Such an engine includes a variable valve mechanism capable of switching a valve characteristic to a first valve characteristic which allows the intake valve to be pre-opened during the exhaust stroke prior to a valve opening time in the intake stroke or allows the exhaust valve to be re-opened during the intake stroke subsequently to the opening/closing thereof during the exhaust stroke, and to a second valve characteristic which allows neither the pre-opening of the intake valve nor the re-opening of the exhaust valve to be performed.